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We prove a new geometric inequality that relates the Arnowitt-Deser-Misner(ADM) mass of initial data to a quasilocal angular momentum of a marginallyouter trapped surface (MOTS) inner boundary. The inequality is expressed interms of a 1-spinor, which satisfies an intrinsic first-order Dirac-typeequation. Furthermore, we show that if the initial data is axisymmetric, thenthe divergence-free vector used to define the quasilocal angular momentumcannot be a Killing field of the generic boundary.

New spinorial mass-quasilocal angular momentum inequality for initial data with marginally outer trapped surface